Hack #41: Estimate Orders of Magnitude

By using rough order-of-magnitude estimates, you can check calculations and estimate whether tasks are even plausible before spending time to plan them more accurately.

Additions and Suggestions

Concrete ideas to modify and expand this hack go here.

Discussion

(see errata)

Links

Links to relevant websites go here.

Errata

In the grape picking example featuring Bart Simpson, the calculations show that Bart can pick 3000 grapes per hour. Working 20-hour days, this would yield 60.000 grapes per day, not 6.000 as stated in the example. Thus Bart would spend just 20 days picking instead of 200. Or have I missed something glaringly obvious here?

The example attempts to prove that Bart Simpson could not theoretically pick 1,000,000 grapes in three months. In the second to last sentence in the third paragraph on page 158, the author's math is incorrect when he states, "So, Bart manages 6,000 (20 X 3,000) grapes a day." The math is off by an order of magnitude and without the mistake we see that Bart in fact could have picked 1,000,000 grapes in 20 days (far less than the 3 month limit).

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In fact, it looks like we missed something glaringly obvious! You're quite right, Bart could pick all those grapes in about three weeks under the given conditions. Thank you for the correction.

If there's a second edition, in addition to correcting the error, we could note that we could have caught this error by making another estimate: three months is about 90 days, which we can round to 100. 1,000,000 grapes divided by 100 is 10,000 grapes/day, and we immediately see that this doesn't match with 3000 grapes per hour with 20 hours of work per day. Bart would only have to work 3 or 4 hours a day. (Maybe those French guys weren't so bad after all!)